Cohomological Finiteness Conditions in Bredon Cohomology

We show that any soluble group $G$ of type Bredon-\FP_{\infty} with respect to the family of all virtually cyclic subgroups such that centralizers of infinite order elements are of type \FP_{\infty} must be virtually cyclic. To prove this, we first reduce the problem to the case of polycyclic groups and then we show that a polycyclic-by-finite group with finitely many conjugacy classes of maximal virtually cyclic subgroups is virtually cyclic. Finally we discuss refinements of this result: we only impose the property Bredon-\FP_n for some $n \leq 3$ and restrict to abelian-by-nilpotent, abelian-by-polycyclic or (nilpotent of class 2)-by-abelian groups.Comment: Corrected a mistake in Lemma 2.4 of the previous version, which had an effect on the results in Section 5 (the condition that all centralisers of infinite order elements are of type $FP_\infty$ was added

The Two-Point Function and the Effective Magnetic Field in Diluted Ising Models on the Cayley Tree

Some results on the two-point function and on the analytic structure of the momenta of the effective fugacity at the origin for a class of diluted ferromagnetic Ising models on the Cayley tree are presented.Comment: 22 page

MACHe3, a prototype for non-baryonic dark matter search: KeV event detection and multicell correlation

Superfluid He3 at ultra-low temperatures (100 microKelvins) is a sensitive medium for the bolometric detection of particles. MACHe3 (MAtrix of Cells of Helium 3) is a project for non-baryonic dark matter search using He3 as a sensitive medium. Simulations made on a high granularity detector show a very good rejection to background signals. A multicell prototype including 3 bolometers has been developed to allow correlations between the cells for background event discrimination. One of the cells contains a low activity Co57 source providing conversion electrons of 7.3 and 13.6 keV to confirm the detection of low energy events. First results on the multicell prototype are presented. A detection threshold of 1 keV has been achieved. The detection of low energy conversion electrons coming from the Co57 source is highlighted as well as the cosmic muon spectrum measurement. The possibility to reject background events by using the correlation among the cells is demonstrated from the simultaneous detection of muons in different cells

On the regularization ambiguities in loop quantum gravity

One of the main achievements of LQG is the consistent quantization of the Wheeler-DeWitt equation which is free of UV problems. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities there is the one associated to the SU(2) unitary rep. used in the diffeomorphism covariant pointsplitting regularization of nonlinear funct. of the connection. This ambiguity is labelled by a halfinteger m and, here, it is referred to as the m-ambiguity. The aim of this paper is to investigate the important implications of this ambiguity./ We first study 2+1 gravity quantized in canonical LQG. Only when the regularization of the quantum constraints is performed in terms of the fundamental rep. of the gauge group one obtains the usual TQFT. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear cut choice in the quantization of the constraints in 2+1 LQG./ We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher unit. rep. quantizations of the Hamiltonian constraint. Although the analysis is not complete in D=3+1--due to the difficulties associated to the definition of the physical inner product--it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find physical solutions associated to spin-two local excitations.Comment: 21 page

A signature of quantum gravity at the source of the seeds of cosmic structure?

This article reviews a recent work by a couple of colleagues and myself about the shortcomings of the standard explanations of the quantum origin of cosmic structure in the inflationary scenario, and a proposal to address them. The point it that in the usual accounts the inhomogeneity and anisotropy of our universe seem to emerge from an exactly homogeneous and isotropic initial state through processes that do not break those symmetries. We argued that some novel aspect of physics must be called upon to able to address the problem in a fully satisfactory way. The proposed approach is inspired on Penrose's ideas regarding an quantum gravity induced, real and dynamical collapse of the wave function.Comment: LateX, (jpconference macros), Prepared for the proceedings the Third International Workshop DICE 2006, " Quantum Mechanics between decoherence and Determinism

Effects of hydrogen/deuterium absorption on the magnetic properties of Co/Pd multilayers

The effects of hydrogen (H2) and deuterium (D2) absorption were studied in two Co/Pd multilayers with perpendicular magnetic anisotropy (PMA) using polarized neutron reflectivity (PNR). PNR was measured in an external magnetic field H applied in the plane of the sample with the magnetization M confined in the plane for {\mu}_o H= 6.0 T and partially out of plane at 0.65 T. Nominal thicknesses of the Co and Pd layers were 2.5 {\AA} and 21 {\AA}, respectively. Because of these small values, the actual layer chemical composition, thickness, and interface roughness parameters were determined from the nuclear scattering length density profile ({\rho}_n) and its derivative obtained from both x-ray reflectivity and PNR, and uncertainties were determined using Monte Carlo analysis. The PNR {\rho}_n showed that although D2 absorption occurred throughout the samples, absorption in the multilayer stack was modest (0.02 D per Pd atom) and thus did not expand. Direct magnetometry showed that H2 absorption decreased the total M at saturation and increased the component of M in the plane of the sample when not at saturation. The PNR magnetic scattering length density ({\rho}_m) revealed that the Pd layers in the multilayer stack were magnetized and that their magnetization was preferentially modified upon D2 absorption. In one sample, a modulation of M with twice the multilayer period was observed at {\mu}_o H= 0.65 T, which increased upon D2 absorption. These results indicate that H2 or D2 absorption decreases both the PMA and total magnetization of the samples. The lack of measurable expansion during absorption indicates that these changes are primarily governed by modification of the electronic structure of the material.Comment: to appear in Physics review B, 201

Self-control in Sparsely Coded Networks

A complete self-control mechanism is proposed in the dynamics of neural networks through the introduction of a time-dependent threshold, determined in function of both the noise and the pattern activity in the network. Especially for sparsely coded models this mechanism is shown to considerably improve the storage capacity, the basins of attraction and the mutual information content of the network.Comment: 4 pages, 6 Postscript figure

A moment based approach to the dynamical solution of the Kuramoto model

We examine the dynamics of the Kuramoto model with a new analytical approach. By defining an appropriate set of moments the dynamical equations can be exactly closed. We discuss some applications of the formalism like the existence of an effective Hamiltonian for the dynamics. We also show how this approach can be used to numerically investigate the dynamical behavior of the model without finite size effects.Comment: 6 pages, 5 figures, Revtex file, to appear in J. Phys.